What is the difference between a problem representation and problem modelling?
I would say these terms are often used interchangeably in AI. When they differ, I would say that problem modeling means finding a mathematical description of the problem, while problem representation means finding a particular way to represent that mathematical formalism.

For example, a list of numbers can be stored (represented) with a linked list, and array list, a hash table, or a self-balancing tree. All of them can produce a faithful model of the list, but if what you want to do is find the order that elements were entered in, the array list or linked list is far faster and more natural. If what you want to do is determine whether certain pieces of information are present in the list, the hash table is fastest. If what you want to do is find ranges of similar elements, the tree is fastest. Essentially, representational choices are engineering problems, while modelling choices are scientific problems.